Saul disobeyed God's command because he feared the people's opinion and chose to listen to them rather than fully obey God's instructions. He allowed the people to keep the best of the livestock instead of destroying everything, as God had commanded.
1 Samuel 15: 24 (RSV) says:
And Saul said to Samuel, "I have sinned; for I have transgressed the commandment of the LORD and your words, because I feared the people and obeyed their voice."